R Notebook
- Implémentation du Perceptron Multi-Couches (PMC)
Caractéristiques du PMC : Structure en couches entièrement connectées :
Un MLP est composé de plusieurs couches de neurones entièrement connectées (Dense layers en Keras). Chaque neurone de la couche précédente est connecté à chaque neurone de la couche suivante. Fonctions d’activation :
Les fonctions d’activation (comme relu ou sigmoid) introduisent de la non-linéarité, permettant au modèle de capturer des relations complexes. Plusieurs couches cachées :
Un MLP a au moins une couche cachée entre la couche d’entrée et la couche de sortie.
# Chargement des bibliothèques utiles pour l'execution de ce notebook
library(ggplot2)
library(reticulate)
library(pROC)Type 'citation("pROC")' for a citation.
Attachement du package : ‘pROC’
L'objet suivant est masqué depuis ‘package:imager’:
ci
Les objets suivants sont masqués depuis ‘package:stats’:
cov, smooth, varlibrary(caret)
suppressPackageStartupMessages(library(caret))
Sys.setenv(TF_CPP_MIN_LOG_LEVEL = "2")
library(keras)library(reticulate)
use_condaenv("tf", conda = "C:/Users/beriv/anaconda3/condabin/conda.bat")
py_config()python: C:/Users/beriv/anaconda3/envs/tf/python.exe
libpython: C:/Users/beriv/anaconda3/envs/tf/python310.dll
pythonhome: C:/Users/beriv/anaconda3/envs/tf
version: 3.10.13 | packaged by Anaconda, Inc. | (main, Sep 11 2023, 13:15:57) [MSC v.1916 64 bit (AMD64)]
Architecture: 64bit
numpy: C:/Users/beriv/anaconda3/envs/tf/Lib/site-packages/numpy
numpy_version: 1.26.3
tensorflow: C:\Users\beriv\ANACON~1\envs\tf\lib\site-packages\tensorflow\__init__.p
NOTE: Python version was forced by use_python() function
# Charger le dataset MNIST
data <- dataset_mnist()
x_train <- data$train$x
y_train <- data$train$y
x_test <- data$test$x
y_test <- data$test$y
# Prétraitement des données
x_train <- array_reshape(x_train, c(nrow(x_train), 28 * 28)) / 255
x_test <- array_reshape(x_test, c(nrow(x_test), 28 * 28)) / 255
y_train <- as.numeric(y_train)
y_test <- as.numeric(y_test)# Séparer les données normales et anormales (par exemple, les 0 sont normaux)
normal_class <- 0
x_train_normal <- x_train[y_train == normal_class, ]
x_test_normal <- x_test[y_test == normal_class, ]
x_test_anomaly <- x_test[y_test != normal_class, ]
# Construire un modèle MLP pour encoder les données normales
model <- keras_model_sequential() %>%
layer_dense(units = 128, activation = 'relu', input_shape = c(28 * 28)) %>%
layer_dense(units = 64, activation = 'relu') %>%
layer_dense(units = 32, activation = 'relu', name = "latent") %>%
layer_dense(units = 64, activation = 'relu') %>%
layer_dense(units = 128, activation = 'relu') %>%
layer_dense(units = 28 * 28, activation = 'sigmoid')
model %>% compile(
optimizer = 'adam',
loss = 'mean_squared_error'
)- Couches entièrement connectées :
Chaque layer_dense représente une couche entièrement connectée. Non-linéarité :
Les fonctions d’activation relu et sigmoid ajoutent la non-linéarité nécessaire. Plusieurs couches cachées :
Le modèle contient plusieurs couches intermédiaires (couches cachées) : 128 → 64 → 32 → 64 → 128. Nombreuses unités (neurones) :
Chaque couche contient un nombre défini d’unités (neurones), comme 128 ou 64.
# Entraîner le modèle uniquement sur les données normales
history <- model %>% fit(
x_train_normal, x_train_normal,
epochs = 30,
batch_size = 256,
validation_split = 0.2
)Epoch 1/30
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19/19 [==============================] - 2s 11ms/step - loss: 0.1527
19/19 [==============================] - 4s 134ms/step - loss: 0.1527 - val_loss: 0.0721
Epoch 2/30
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19/19 [==============================] - 0s 13ms/step - loss: 0.0684
19/19 [==============================] - 0s 26ms/step - loss: 0.0684 - val_loss: 0.0631
Epoch 3/30
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19/19 [==============================] - 0s 9ms/step - loss: 0.0606
19/19 [==============================] - 1s 32ms/step - loss: 0.0606 - val_loss: 0.0547
Epoch 4/30
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19/19 [==============================] - 0s 9ms/step - loss: 0.0514
19/19 [==============================] - 1s 29ms/step - loss: 0.0514 - val_loss: 0.0458
Epoch 5/30
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19/19 [==============================] - 0s 13ms/step - loss: 0.0446
19/19 [==============================] - 1s 29ms/step - loss: 0.0446 - val_loss: 0.0418
Epoch 6/30
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19/19 [==============================] - 1s 29ms/step - loss: 0.0410 - val_loss: 0.0381
Epoch 7/30
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19/19 [==============================] - 0s 12ms/step - loss: 0.0371
19/19 [==============================] - 1s 30ms/step - loss: 0.0371 - val_loss: 0.0346
Epoch 8/30
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19/19 [==============================] - 0s 9ms/step - loss: 0.0339
19/19 [==============================] - 1s 29ms/step - loss: 0.0339 - val_loss: 0.0323
Epoch 9/30
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19/19 [==============================] - 0s 12ms/step - loss: 0.0317
19/19 [==============================] - 1s 30ms/step - loss: 0.0317 - val_loss: 0.0304
Epoch 10/30
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19/19 [==============================] - 0s 13ms/step - loss: 0.0297
19/19 [==============================] - 1s 31ms/step - loss: 0.0297 - val_loss: 0.0287
Epoch 11/30
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19/19 [==============================] - 0s 13ms/step - loss: 0.0280
19/19 [==============================] - 1s 29ms/step - loss: 0.0280 - val_loss: 0.0270
Epoch 12/30
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Epoch 13/30
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Epoch 14/30
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Epoch 15/30
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19/19 [==============================] - 0s 8ms/step - loss: 0.0231
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Epoch 16/30
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19/19 [==============================] - 0s 9ms/step - loss: 0.0222
19/19 [==============================] - 0s 22ms/step - loss: 0.0222 - val_loss: 0.0218
Epoch 17/30
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19/19 [==============================] - 0s 8ms/step - loss: 0.0214
19/19 [==============================] - 0s 24ms/step - loss: 0.0214 - val_loss: 0.0211
Epoch 18/30
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Epoch 19/30
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19/19 [==============================] - 0s 8ms/step - loss: 0.0202
19/19 [==============================] - 0s 25ms/step - loss: 0.0202 - val_loss: 0.0201
Epoch 20/30
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19/19 [==============================] - 0s 11ms/step - loss: 0.0197
19/19 [==============================] - 1s 29ms/step - loss: 0.0197 - val_loss: 0.0196
Epoch 21/30
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19/19 [==============================] - 0s 8ms/step - loss: 0.0192
19/19 [==============================] - 0s 20ms/step - loss: 0.0192 - val_loss: 0.0195
Epoch 22/30
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19/19 [==============================] - 0s 8ms/step - loss: 0.0188
19/19 [==============================] - 0s 24ms/step - loss: 0.0188 - val_loss: 0.0191
Epoch 23/30
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19/19 [==============================] - 0s 9ms/step - loss: 0.0185
19/19 [==============================] - 0s 24ms/step - loss: 0.0185 - val_loss: 0.0186
Epoch 24/30
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19/19 [==============================] - 0s 8ms/step - loss: 0.0181
19/19 [==============================] - 0s 23ms/step - loss: 0.0181 - val_loss: 0.0181
Epoch 25/30
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19/19 [==============================] - 0s 9ms/step - loss: 0.0176
19/19 [==============================] - 1s 30ms/step - loss: 0.0176 - val_loss: 0.0177
Epoch 26/30
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19/19 [==============================] - 0s 11ms/step - loss: 0.0172
19/19 [==============================] - 0s 22ms/step - loss: 0.0172 - val_loss: 0.0174
Epoch 27/30
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19/19 [==============================] - 0s 23ms/step - loss: 0.0170 - val_loss: 0.0170
Epoch 28/30
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19/19 [==============================] - 0s 8ms/step - loss: 0.0166
19/19 [==============================] - 0s 24ms/step - loss: 0.0166 - val_loss: 0.0168
Epoch 29/30
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19/19 [==============================] - 0s 8ms/step - loss: 0.0164
19/19 [==============================] - 0s 25ms/step - loss: 0.0164 - val_loss: 0.0166
Epoch 30/30
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19/19 [==============================] - 0s 27ms/step - loss: 0.0161 - val_loss: 0.0162# Calculer l'erreur de reconstruction pour les données normales et anormales
reconstruction_error <- function(model, data) {
reconstructed <- model %>% predict(data)
errors <- rowSums((data - reconstructed)^2)
return(errors)
}normal_errors <- reconstruction_error(model, x_test_normal)
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31/31 [==============================] - 0s 6ms/stepanomaly_errors <- reconstruction_error(model, x_test_anomaly)
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282/282 [==============================] - 1s 3ms/step# Définir un seuil pour détecter les anomalies
threshold <- quantile(normal_errors, 0.95)
# Identifier les anomalies
is_anomaly <- function(errors, threshold) {
return(errors > threshold)
}
normal_anomalies <- is_anomaly(normal_errors, threshold)
anomaly_detected <- is_anomaly(anomaly_errors, threshold)
# Résumé des résultats
cat("Seuil d'anomalie:", threshold, "\n")Seuil d'anomalie: 24.32507 cat("Taux de détection d'anomalies parmi les données normales:", mean(normal_anomalies), "\n")Taux de détection d'anomalies parmi les données normales: 0.05 cat("Taux de détection d'anomalies parmi les anomalies:", mean(anomaly_detected), "\n")Taux de détection d'anomalies parmi les anomalies: 0.9900222 # Simuler des prédictions et des labels réels
set.seed(42)
actual <- c(rep(0, 50), rep(1, 50)) # Labels réels : 50 normaux, 50 anomalies
predicted <- c(rep(0, 45), rep(1, 5), rep(0, 10), rep(1, 40)) # Prédictions du modèle
# Afficher la matrice de confusion
conf_matrix <- confusionMatrix(as.factor(predicted), as.factor(actual))
print(conf_matrix)Confusion Matrix and Statistics
Reference
Prediction 0 1
0 45 10
1 5 40
Accuracy : 0.85
95% CI : (0.7647, 0.9135)
No Information Rate : 0.5
P-Value [Acc > NIR] : 2.413e-13
Kappa : 0.7
Mcnemar's Test P-Value : 0.3017
Sensitivity : 0.9000
Specificity : 0.8000
Pos Pred Value : 0.8182
Neg Pred Value : 0.8889
Prevalence : 0.5000
Detection Rate : 0.4500
Detection Prevalence : 0.5500
Balanced Accuracy : 0.8500
'Positive' Class : 0
# Calculer et afficher le rapport de classification
precision <- conf_matrix$byClass["Precision"]
recall <- conf_matrix$byClass["Recall"]
f1_score <- 2 * (precision * recall) / (precision + recall)
cat("\nRapport de Classification :\n")
Rapport de Classification :cat("Précision :", round(precision, 2), "\n")Précision : 0.82 cat("Rappel :", round(recall, 2), "\n")Rappel : 0.9 cat("F1-Score :", round(f1_score, 2), "\n")F1-Score : 0.86 # Aplatir les images pour obtenir des vecteurs
x_train_flat <- array_reshape(x_train, c(nrow(x_train), 28 * 28)) / 255
x_test_flat <- array_reshape(x_test, c(nrow(x_test), 28 * 28)) / 255
# Calculer les moyennes et écarts-types sur l'ensemble d'entraînement
train_mean <- colMeans(x_train_flat, na.rm = TRUE)
train_sd <- apply(x_train_flat, 2, function(x) sd(x, na.rm = TRUE))
# Éviter la division par zéro en remplaçant les écarts-types nuls par une petite valeur
train_sd[train_sd < 0.01] <- 0.01
# Calcul des scores Z
z_scores <- abs(sweep(x_test_flat, 2, train_mean, "-") / train_sd)
# Définir un seuil basé sur les données normales
threshold <- quantile(rowMeans(z_scores), 0.95) # Seuil au 99e percentile
anomalies <- rowMeans(z_scores > threshold) > 0
cat("Nombre d'anomalies détectées :", sum(anomalies), "\n")Nombre d'anomalies détectées : 10000 # Afficher le nombre d'anomalies détectées
cat("Nombre d'anomalies détectées :", sum(anomalies, na.rm = TRUE), "\n")Nombre d'anomalies détectées : 10000 # Visualiser une anomalie
if (any(anomalies, na.rm = TRUE)) {
idx <- which(anomalies)[1] # Index de la première anomalie
image(matrix(x_test[idx, , ], 28, 28), col = gray.colors(256), main = "Anomalie détectée")
}
summary(train_mean) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000000 0.0004864 0.0283191 0.1306605 0.2701763 0.5472690 summary(train_sd) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000001 0.017972 0.144604 0.193221 0.394989 0.446329 DISTANCE DE MAHALANOBIS
x_train <- mnist$train$x
x_test <- mnist$test$x
# Aplatir les images pour obtenir des vecteurs
x_train_flat <- array_reshape(x_train, c(nrow(x_train), 28 * 28)) / 255
x_test_flat <- array_reshape(x_test, c(nrow(x_test), 28 * 28)) / 255
# Vérifier et éliminer les colonnes avec faible variance
keep <- apply(x_train_flat, 2, var) > 1e-6
x_train_flat <- x_train_flat[, keep]
x_test_flat <- x_test_flat[, keep]
# Réduction de dimension avec PCA (facultatif, si les données sont encore trop corrélées)
library(stats)
pca_result <- prcomp(x_train_flat, center = TRUE, scale. = TRUE)
# Conserver les 100 premières composantes
num_components <- 100
x_train_pca <- pca_result$x[, 1:num_components]
x_test_pca <- predict(pca_result, newdata = x_test_flat)[, 1:num_components]
# Calculer la matrice de covariance et son inverse avec régularisation
epsilon <- 1e-6 # Petite valeur pour régulariser
cov_matrix <- cov(x_train_pca) + diag(epsilon, ncol(x_train_pca))
inv_cov_matrix <- solve(cov_matrix)
# Calculer la moyenne des données d'entraînement
mean_vector <- colMeans(x_train_pca)
# Fonction pour calculer la distance de Mahalanobis
mahalanobis_distance <- function(x, mean, inv_cov) {
diff <- x - mean
sqrt(rowSums((diff %*% inv_cov) * diff))
}
# Calculer les distances de Mahalanobis pour les données de test
distances <- mahalanobis_distance(x_test_pca, mean_vector, inv_cov_matrix)
# Définir un seuil basé sur le quantile des distances
threshold <- quantile(distances, 0.99) # Seuil au 99e percentile
# Identifier les anomalies
anomalies <- distances > threshold
cat("Nombre d'anomalies détectées :", sum(anomalies), "\n")Nombre d'anomalies détectées : 100 # Visualiser une anomalie
if (any(anomalies)) {
idx <- which(anomalies)[1] # Index de la première anomalie
image(matrix(x_test[idx, , ], 28, 28), col = gray.colors(256), main = "Anomalie détectée")
}
str(x_train) int [1:60000, 1:28, 1:28] 0 0 0 0 0 0 0 0 0 0 ...# Chargement les bibliothèques nécessaires
library(imager)# Étape 1 : Aplatir les images
x_test_flat <- apply(x_test, 1, function(image) {
as.vector(image) # Aplatir chaque matrice en vecteur
})
x_test_flat <- t(x_test_flat) # Transposer pour obtenir (N x 784)
cat("Dimensions de x_test_flat :", dim(x_test_flat), "\n")Dimensions de x_test_flat : 10000 784 # Étape 2 : Générer les anomalies
apply_transformations <- function(image) {
image_matrix <- matrix(image, nrow = 28, ncol = 28)
transformed_image <- imrotate(as.cimg(image_matrix), angle = sample(c(-45, 45), 1)) # Rotation large
scaled_image <- imresize(transformed_image, scale = runif(1, 0.5, 2.0)) # Échelle variable
noisy_image <- scaled_image + rnorm(length(scaled_image), mean = 0, sd = 0.1) # Bruit
return(as.vector(as.numeric(noisy_image)))
}
# Appliquer une transformation (exemple : rotation et mise à l'échelle)
rotated_image <- imrotate(as.cimg(image_matrix), angle = sample(c(-30, 30), 1)) # RotationErreur : objet 'image_matrix' introuvable# Charger les bibliothèques nécessaires
library(keras)
library(caret)
# Étape 1 : Préparer les données
# Charger le dataset MNIST
data <- dataset_mnist()
x_train <- data$train$x
y_train <- data$train$y
x_test <- data$test$x
y_test <- data$test$y
# Aplatir les images en vecteurs 784 et normaliser
x_train_flat <- apply(x_train, 1, function(image) as.vector(image)) / 255
x_train_flat <- t(x_train_flat)
x_test_flat <- apply(x_test, 1, function(image) as.vector(image)) / 255
x_test_flat <- t(x_test_flat)
# Étape 2 : Générer les anomalies
apply_transformations <- function(image) {
# Reshape l'image aplatie en une matrice 28x28
image_matrix <- matrix(image, nrow = 28, ncol = 28)
# Appliquer une transformation (exemple : rotation et mise à l'échelle)
rotated_image <- imrotate(as.cimg(image_matrix), angle = sample(c(-30, 30), 1)) # Rotation
scaled_image <- imresize(rotated_image, scale = 1.2) # Mise à l'échelle
# Remettre au format 28x28 (padding ou recadrage si nécessaire)
scaled_image <- resize(scaled_image, size_x = 28, size_y = 28)
return(as.vector(as.numeric(scaled_image))) # Retourner le vecteur aplati
}
# Filtrer les données normales : toutes les images nettes, non transformées
x_train_normal <- x_train_flat
x_test_normal <- x_test_flat
# Créer des anomalies en appliquant des transformations sur x_test_flat
set.seed(42) # Fixer une graine pour la reproductibilité
x_test_anomaly <- t(apply(x_test_flat, 1, apply_transformations))
# Étape 3 : Définir et entraîner l'autoencodeur
model <- keras_model_sequential() %>%
layer_dense(units = 128, activation = 'relu', input_shape = c(28 * 28)) %>%
layer_dense(units = 64, activation = 'relu') %>%
layer_dense(units = 32, activation = 'relu', name = "latent") %>%
layer_dense(units = 64, activation = 'relu') %>%
layer_dense(units = 128, activation = 'relu') %>%
layer_dense(units = 28 * 28, activation = 'sigmoid')
model %>% compile(
optimizer = 'adam',
loss = 'mean_squared_error'
)
# Entraîner uniquement sur les données normales
history <- model %>% fit(
x_train_normal, x_train_normal,
epochs = 30,
batch_size = 256,
validation_split = 0.2
)Epoch 1/30
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188/188 [==============================] - 2s 8ms/step - loss: 0.0700
188/188 [==============================] - 3s 13ms/step - loss: 0.0700 - val_loss: 0.0439
Epoch 2/30
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188/188 [==============================] - 2s 8ms/step - loss: 0.0361
188/188 [==============================] - 2s 10ms/step - loss: 0.0361 - val_loss: 0.0294
Epoch 3/30
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188/188 [==============================] - 2s 9ms/step - loss: 0.0257
188/188 [==============================] - 2s 11ms/step - loss: 0.0257 - val_loss: 0.0234
Epoch 4/30
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188/188 [==============================] - 2s 10ms/step - loss: 0.0219
188/188 [==============================] - 2s 12ms/step - loss: 0.0219 - val_loss: 0.0210
Epoch 5/30
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188/188 [==============================] - 2s 11ms/step - loss: 0.0198
188/188 [==============================] - 2s 13ms/step - loss: 0.0198 - val_loss: 0.0193
Epoch 6/30
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Epoch 7/30
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188/188 [==============================] - 2s 8ms/step - loss: 0.0170
188/188 [==============================] - 2s 10ms/step - loss: 0.0170 - val_loss: 0.0167
Epoch 8/30
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188/188 [==============================] - 2s 8ms/step - loss: 0.0161
188/188 [==============================] - 2s 10ms/step - loss: 0.0161 - val_loss: 0.0158
Epoch 9/30
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188/188 [==============================] - 2s 8ms/step - loss: 0.0153
188/188 [==============================] - 2s 10ms/step - loss: 0.0153 - val_loss: 0.0151
Epoch 10/30
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188/188 [==============================] - 2s 8ms/step - loss: 0.0146
188/188 [==============================] - 2s 10ms/step - loss: 0.0146 - val_loss: 0.0145
Epoch 11/30
1/188 [..............................] - ETA: 1s - loss: 0.0143
8/188 [>.............................] - ETA: 1s - loss: 0.0142
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188/188 [==============================] - 2s 10ms/step - loss: 0.0140
188/188 [==============================] - 2s 12ms/step - loss: 0.0140 - val_loss: 0.0139
Epoch 12/30
1/188 [..............................] - ETA: 1s - loss: 0.0136
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188/188 [==============================] - 2s 9ms/step - loss: 0.0134
188/188 [==============================] - 2s 11ms/step - loss: 0.0134 - val_loss: 0.0135
Epoch 13/30
1/188 [..............................] - ETA: 0s - loss: 0.0132
6/188 [..............................] - ETA: 1s - loss: 0.0135
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188/188 [==============================] - 2s 10ms/step - loss: 0.0130
188/188 [==============================] - 2s 11ms/step - loss: 0.0130 - val_loss: 0.0131
Epoch 14/30
1/188 [..............................] - ETA: 0s - loss: 0.0130
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188/188 [==============================] - 2s 10ms/step - loss: 0.0126
188/188 [==============================] - 2s 11ms/step - loss: 0.0126 - val_loss: 0.0126
Epoch 15/30
1/188 [..............................] - ETA: 0s - loss: 0.0120
7/188 [>.............................] - ETA: 1s - loss: 0.0124
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188/188 [==============================] - 2s 8ms/step - loss: 0.0123
188/188 [==============================] - 2s 10ms/step - loss: 0.0123 - val_loss: 0.0123
Epoch 16/30
1/188 [..............................] - ETA: 1s - loss: 0.0116
8/188 [>.............................] - ETA: 1s - loss: 0.0121
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188/188 [==============================] - 2s 8ms/step - loss: 0.0120
188/188 [==============================] - 2s 10ms/step - loss: 0.0120 - val_loss: 0.0121
Epoch 17/30
1/188 [..............................] - ETA: 1s - loss: 0.0117
8/188 [>.............................] - ETA: 1s - loss: 0.0119
11/188 [>.............................] - ETA: 2s - loss: 0.0119
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188/188 [==============================] - 2s 8ms/step - loss: 0.0117
188/188 [==============================] - 2s 10ms/step - loss: 0.0117 - val_loss: 0.0118
Epoch 18/30
1/188 [..............................] - ETA: 1s - loss: 0.0110
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188/188 [==============================] - 1s 8ms/step - loss: 0.0114
188/188 [==============================] - 2s 10ms/step - loss: 0.0114 - val_loss: 0.0115
Epoch 19/30
1/188 [..............................] - ETA: 1s - loss: 0.0121
8/188 [>.............................] - ETA: 1s - loss: 0.0111
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188/188 [==============================] - 2s 10ms/step - loss: 0.0112
188/188 [==============================] - 2s 12ms/step - loss: 0.0112 - val_loss: 0.0113
Epoch 20/30
1/188 [..............................] - ETA: 0s - loss: 0.0104
7/188 [>.............................] - ETA: 1s - loss: 0.0109
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188/188 [==============================] - 2s 9ms/step - loss: 0.0109
188/188 [==============================] - 2s 11ms/step - loss: 0.0109 - val_loss: 0.0111
Epoch 21/30
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188/188 [==============================] - 2s 9ms/step - loss: 0.0107
188/188 [==============================] - 2s 11ms/step - loss: 0.0107 - val_loss: 0.0108
Epoch 22/30
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188/188 [==============================] - 2s 9ms/step - loss: 0.0106
188/188 [==============================] - 2s 11ms/step - loss: 0.0106 - val_loss: 0.0107
Epoch 23/30
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188/188 [==============================] - 2s 8ms/step - loss: 0.0104
188/188 [==============================] - 2s 10ms/step - loss: 0.0104 - val_loss: 0.0106
Epoch 24/30
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188/188 [==============================] - 2s 8ms/step - loss: 0.0102
188/188 [==============================] - 2s 10ms/step - loss: 0.0102 - val_loss: 0.0104
Epoch 25/30
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188/188 [==============================] - 1s 8ms/step - loss: 0.0101
188/188 [==============================] - 2s 10ms/step - loss: 0.0101 - val_loss: 0.0103
Epoch 26/30
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188/188 [==============================] - 1s 8ms/step - loss: 0.0100
188/188 [==============================] - 2s 10ms/step - loss: 0.0100 - val_loss: 0.0101
Epoch 27/30
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188/188 [==============================] - 2s 10ms/step - loss: 0.0098
188/188 [==============================] - 2s 11ms/step - loss: 0.0098 - val_loss: 0.0099
Epoch 28/30
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188/188 [==============================] - 2s 9ms/step - loss: 0.0097
188/188 [==============================] - 2s 12ms/step - loss: 0.0097 - val_loss: 0.0104
Epoch 29/30
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188/188 [==============================] - 2s 10ms/step - loss: 0.0096
188/188 [==============================] - 2s 12ms/step - loss: 0.0096 - val_loss: 0.0097
Epoch 30/30
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188/188 [==============================] - 2s 10ms/step - loss: 0.0094
188/188 [==============================] - 2s 11ms/step - loss: 0.0094 - val_loss: 0.0096# Étape 4 : Calculer les erreurs de reconstruction
reconstruction_error <- function(model, data) {
reconstructed <- model %>% predict(data)
errors <- rowSums((data - reconstructed)^2)
return(errors)
}
normal_errors <- reconstruction_error(model, x_test_normal)
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313/313 [==============================] - 1s 3ms/step
313/313 [==============================] - 1s 3ms/stepanomaly_errors <- reconstruction_error(model, x_test_anomaly)
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313/313 [==============================] - 1s 2ms/step# Définir un seuil basé sur les données normales
threshold <- quantile(normal_errors, 0.95)
# Détecter les anomalies
is_anomaly <- function(errors, threshold) {
return(errors > threshold)
}
normal_anomalies <- is_anomaly(normal_errors, threshold)
anomaly_detected <- is_anomaly(anomaly_errors, threshold)
# Étape 5 : Évaluer les performances
cat("Seuil d'anomalie :", threshold, "\n")Seuil d'anomalie : 15.37555 cat("Taux de détection des anomalies parmi les données normales :", mean(normal_anomalies), "\n")Taux de détection des anomalies parmi les données normales : 0.05 cat("Taux de détection des anomalies parmi les anomalies :", mean(anomaly_detected), "\n")Taux de détection des anomalies parmi les anomalies : 0.0027 # Tracer une courbe ROC
errors <- c(normal_errors, anomaly_errors)
labels <- c(rep(0, length(normal_errors)), rep(1, length(anomaly_errors)))
roc_obj <- roc(labels, errors)Setting levels: control = 0, case = 1
Setting direction: controls > casesplot(roc_obj, main = "Courbe ROC", col = "blue", lwd = 2)
abline(a = 0, b = 1, col = "gray", lty = 2)
cat("AUC :", auc(roc_obj), "\n")AUC : 0.5917695 # Étape 5 : Évaluer les performances
cat("Seuil d'anomalie :", threshold, "\n")Seuil d'anomalie : 15.37555 cat("Taux de détection des anomalies parmi les données normales :", mean(normal_anomalies), "\n")Taux de détection des anomalies parmi les données normales : 0.05 cat("Taux de détection des anomalies parmi les anomalies :", mean(anomaly_detected), "\n")Taux de détection des anomalies parmi les anomalies : 0.0027 library(plotly)
# Vérifier que les métriques de perte sont disponibles
if (!is.null(history$metrics$loss) && !is.null(history$metrics$val_loss)) {
# Extraire les données de perte
train_loss <- as.numeric(history$metrics$loss)
val_loss <- as.numeric(history$metrics$val_loss)
epochs <- seq_along(train_loss)
# Créer un graphique interactif avec `plotly`
fig <- plot_ly() %>%
add_trace(x = ~epochs, y = ~train_loss, type = 'scatter', mode = 'lines+markers',
name = 'Entraînement', line = list(color = 'blue'), marker = list(color = 'blue')) %>%
add_trace(x = ~epochs, y = ~val_loss, type = 'scatter', mode = 'lines+markers',
name = 'Validation', line = list(color = 'red'), marker = list(color = 'red')) %>%
layout(
title = "Courbe de perte pendant l'entraînement",
xaxis = list(title = "Époques"),
yaxis = list(title = "Perte (Loss)"),
legend = list(x = 0.1, y = 0.9)
)
# Afficher dans l'onglet Viewer
fig
} else {
cat("Erreur : Les métriques de perte 'loss' ou 'val_loss' sont introuvables dans 'history'.\n")
}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